Question: Tiffany is 32 years younger than Ishaan. For the last two years, Ishaan and Tiffany have been going to the same school. Eleven years ago, Ishaan was 5 times older than Tiffany. How old is Ishaan now?
Explanation: We can use the given information to write down two equations that describe the ages of Ishaan and Tiffany. Let Ishaan's current age be $i$ and Tiffany's current age be $t$ The information in the first sentence can be expressed in the following equation: $i = t + 32$ Eleven years ago, Ishaan was $i - 11$ years old, and Tiffany was $t - 11$ years old. The information in the second sentence can be expressed in the following equation: $i - 11 = 5(t - 11)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $t$ and substitute it into our second equation. Solving our first equation for $t$ , we get: $t = i - 32$ . Substituting this into our second equation, we get the equation: $i - 11 = 5($ $(i - 32)$ $ -$ $ 11)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 11 = 5i - 215$ Solving for $i$ , we get: $4 i = 204$ $i = 51$.